Graphene-based metasurface solar absorber design with absorption prediction using machine learning

Solar absorber is required to absorb most of the energy of the solar spectral irradiance. We propose a graphene-based solar absorber design with two different metasurfaces to improve this absorption and increase the efficiency of the solar absorber. The metasurfaces are selected based on their symmetrical/asymmetrical nature (O-shape and L-shape). The O-shape metasurface design is showing better performance over the L-shape metasurface design. The absorption performance is also compared with AM 1.5 solar spectral irradiance to show the effectiveness of the solar absorber. The absorption values are also enhanced by varying the parameters like resonator thickness and substrate thickness. The proposed solar absorber design gives maximum absorption in the ultraviolet and visible range. Furthermore, the design is also showing a high and similar absorption rate over a wide angle of incidence. The absorption of O-shape metasurface design is also predicted using machine learning. 1D-Convolutional Neural Network Regression is used to develop a Machine Learning model to determine absorption values of intermediate wavelength for assorted values of angle of incidence, resonator thickness, and substrate thickness. The results of experiments reveal that absorption values may be predicted with a high degree of accuracy. The proposed absorber with its high absorbing capacity can be applied for green energy applications.

Energy demand is increasing day by day because of rapid industrialization and an increase in household energy consumption. Renewable and clean energy is the ultimate solution for these increasing energy demands as it is not affecting the environment. Solar energy is one of the best clean, renewable natural sources because of its ease of availability. It can be one of the best ways to cope up with the increasing energy demand. Still to make the solar energy utilization more efficient. Solar energy can also be easily converted into other forms of energy which can be applied for the designing purpose of solar cells, photovoltaic devices, and solar absorbers, etc. A perfect absorber is quietly prudent for various applications consisting of solar energy harvesting, light modulation, and sensing, etc. [1][2][3][4][5][6] . Metamaterials have attracted a lot of attention and they are the unique candidate due to their unique electro-optical characteristics and compact size rather than bulky optical devices [7][8][9][10][11][12] . Due to this, they have various applications comprising from polarizers, detectors to absorbers [13][14][15][16][17] each working at various operating frequencies, i.e., microwave, terahertz, ultraviolet, visible, infrared, etc. [18][19][20][21][22] .
Graphene is also an essential element for the advancement of physics, photonics-like fields. From the available research on graphene, we can say that graphene is a two-dimensional element with an astonishing electrocrystal characteristic that plays a major role in designing applications that are based on recent physics and other concerned domains. To conclude, graphene is a new group of elements that is only an atom-thick but has helped to obtain the results in the subdomain of physics known as low magnitude physics 23 . Graphene has remarkable electro-optical, thermal, mechanical properties which can be applied with a solar absorber 24 . As per the research, filtered graphene sheet is highly transparent and flexible because graphene's every single layer with refractivity of 0.1% absorbs up to 2.3% of white light 25 . Studies also indicate that as the no. of graphene sheet increases so does the absorption rate 26 33 .
In this paper, we have proposed a high absorption graphene-based absorber that is broadband for the ultraviolet and visible range. We have also carried out a detailed comparative analysis of the o-shape metasurface design that gives better absorption by varying the different physical parameters of the design. The second section presents the graphene-based metasurface design, the third section presents parametric analysis and the fourth section presents the design of 1D-Convolutional Neural Network (CNN) regression model to predict the absorption values of intermediate wavelengths and corresponding experimental results. The concluding remarks are presented in the fifth section.

Graphene-based metasurface design
Graphene-based metasurface absorber design is presented in Fig. 1 for two different metasurfaces (O-shape metasurface and L-shape metasurface). The reason for selecting these two shapes is because one is symmetrical design and the other one is asymmetrical design. The design is made with a gold resonator based on SiO 2 substrate with graphene monolayer as a spacer sandwiched between the two layers. The two different metasurfaces www.nature.com/scientificreports/ are created by changing the shape of the metasurface as presented in their top views (Fig. 1a,d). The side views and 3d views are also presented in the schematic. The light is falling on the top of the resonator which is an O-shape and L-shape for two metasurface absorbers. The O-shape metasurface absorber is increasing the inductance by connected resonator shape and it is also symmetrical. The L-shape metasurface is having a change in inductance and capacitance compared to the O-shape metasurface as there is no connected path like the O-shape metasurface. The L-shape is also not symmetric which gives rise to the polarization sensitiveness 34 compared to the symmetric shape of the O-shape metasurface which is polarization insensitive. The metasurface absorber structure presented in Fig. 1 is a periodic structure with a period of 3 µm in both directions. The different geometrical parameter values presented in Fig. 1 are L: 3 µm, L1: 2.4 µm, L2: 1 µm, L3: 2.4 µm, L4: 2.2 µm hs: 1 µm; hg: 0.6 µm and the graphene monolayer thickness is 0.34 nm. The use of graphene material is essential in this design because the graphene with its high conductivity contributes to enhancing the absorption and achieving the broadband design. The conductivity ( σ s ) of graphene depends on graphene chemical potential ( µ c ) and is presented in Eqs. (1)(2)(3)(4).
The different parameters used in the equations are: scattering rate (Γ), Reduced plank constant ( ℏ ), Boltzmann constant (k B ), Electron relaxation time (τ −1 ) and is the thickness of graphene which is 0.34 nm. The fabrication of graphene monolayer sheets can be done with chemical vapour deposition (CVD) 35 or cleavage technique 36 or lithography 37 .
The metasurface designs are simulated using the Finite Element Method (FEM) based COMSOL Simulator and the results in the form of absorption are presented and compared [38][39][40][41][42][43][44][45][46] in Fig. 2 and Table 1. The light is falling from the top of the resonator structure and periodic boundary conditions are used for the simulations. The meshing condition of the structure is set as tetrahedral Delaunay tessellation. The absorption response for O-shape metasurface absorber design and L-shape metasurface absorber design is presented in Fig. 2a,b respectively. The blue colour region shows the absorption plot and its values on the left-hand side for our proposed design and the orange colour shows the AM 1.5 spectral irradiance plot with its values on the right-hand side. The absorption response is also compared with AM 1.5 spectral irradiance. The comparison with irradiance shows the effectiveness of the absorber as more absorption in high irradiance shows the higher efficiency of the absorber. The response shows that the O-shape metasurface absorber design is showing near to unity absorption for the high spectral irradiance in the visible region which makes the O-shape metasurface more effective in solar energy harvesting applications. The L-shape metasurface absorber is having less absorption for the high spectral irradiance region as presented in Fig. 2b.
We have also analyzed the electric field for O-shape metasurface design (Fig. 3) to observe and verify the absorption in terms of the electric field. The selection of three different wavelengths is carried out to observe the electric field at different absorption levels. The three wavelengths selected are 0.5 µm, 0.8 µm, and 1.2 µm. The results clearly show that for the initial wavelength the electric field is more around the resonator and as the wavelength increases the absorption increases in the substrate. The electric field is measured in V/m and its values are given in a scale on the right-hand side of Fig. 3. The red colour indicated the high electric field (6.6 × 10 6 V/m).

Parametric analysis
The absorption of the absorber is dependent on its geometrical parameters so we have applied the parametric analysis of two geometrical parameters namely substrate thickness and resonator thickness (Fig. 4a,b). We have also varied the angle of incidence and graphene chemical potential (Fig. 4c,d) to observe its effect on absorption. The analysis is presented for the 0.2 to 1.2 µm wavelength range. The resonator thickness is varied for 0.6 to 1.4 µm and substrate thickness is varied from 0.2 to 1 µm and absorption results are presented in Fig. 4a,b respectively. The colour plot for the variation is presented as an inset in the figure for a better understanding of the results. The variation in resonator thickness clearly shows that for 0.6 µm value, the absorption is highest in overall best with more than 92% average absorption in visible and ultraviolet regions. As we increase the resonator thickness greater than 0.6 µm, the absorption decreases in the visible and ultraviolet region but increase in the infrared region because the inductance effect is increased as the thickness of the resonator is increasing which results in a change in absorption in higher wavelength. The substrate thickness is varied from 0.2 to 1 µm and the results clearly show that as the thickness is increased, the absorption is increasing and the best values are available for 1 µm thickness. The reason for the increase in absorption is because the higher thickness increases the area of the substrate, which increases the absorption in the substrate. The resonator thickness of 0.6 µm and substrate thickness is 1 µm is fixed after this parametric analysis.
The graphene chemical potential is varied from 0.1 to 0.9 eV and we are getting similar absorption for all the variation which clearly show that at visible and ultraviolet wavelength range the effect of graphene's chemical www.nature.com/scientificreports/  www.nature.com/scientificreports/ potential is minimum. The angle of incidence is very important for designing solar absorbers so we have also varied the angle of incidence from 0° to 80° and the results clearly show that we are getting a wide-angle of incidence and the absorption is almost the same for all angles except 30° and 80°. The results clearly show that for angle of incidence 30° and 80°, the average absorption is more than 60% and for the rest of the angles it is more than 92%. These parameter variations clearly show that graphene chemical potential has minimum effect in absorption response while the wide-angle of incidence is also achieved for the angle of incidence variation of light falling on the structure.

Machine learning (1D-CNN regression model for prediction)
Machine Randomly selected records are used to evaluate the performance of Machine Learning model which is trained using remaining records of simulated data. R 2 score is used as a metric to evaluate the prediction accuracy of regression models. R 2 score is calculated using Eq. (5). www.nature.com/scientificreports/ www.nature.com/scientificreports/ Here, SS res is the sum of squares of the residual errors and SS tot is the total sum of the errors and N is the number of testing records.
All R 2 score values are rounded off to four decimal places while representing the results. Reason for using higher degree polynomial features for training 1D-CNN regressor models is explained in supplementary material with the help of Supplementary Fig. S1.    www.nature.com/scientificreports/

Conclusion
In conclusion, we have presented the two different graphene-metasurface absorber designs and obtained the high absorption for a broadband range including the ultraviolet and visible range. The O-shape design achieves absorption of 91% and 94% for the ultraviolet and visible range, respectively. We have also carried out the detailed analysis by varying the physical parameters such as resonator thickness and substrate thickness which slightly affects the absorption rate. The absorption response also remains unchanged for the wide angle of incidence. The response also remains the same with respect to the variation in graphene chemical potential. It is demonstrated using experimental results that, 1D-CNN Regression is an efficient method for building the prediction model. It can predict absorption values of intermediate wavelengths with high accuracy (more than 0.999 R 2 Score). It is also observed that high prediction accuracy is achieved in most of the cases when model is built using higher polynomial degree features.

Data availability
The data will be made available at a reasonable request to the corresponding author.